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<div class="header">
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<a href="#func-members">Functions</a>  </div>
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<div class="title">Geometric Algebra operations</div>  </div>
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<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:ga24f8d65c6ffeb2e1468c20f3d1b74a35"><td class="memTemplParams" colspan="2"><a class="anchor" id="ga24f8d65c6ffeb2e1468c20f3d1b74a35"></a>
template&lt;class L , class R &gt; </td></tr>
<tr class="memitem:ga24f8d65c6ffeb2e1468c20f3d1b74a35"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="structgaalet_1_1addition.html">gaalet::addition</a>&lt; L, R &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__ga__ops.html#ga24f8d65c6ffeb2e1468c20f3d1b74a35">operator+</a> (const <a class="el" href="structgaalet_1_1expression.html">gaalet::expression</a>&lt; L &gt; &amp;l, const <a class="el" href="structgaalet_1_1expression.html">gaalet::expression</a>&lt; R &gt; &amp;r)</td></tr>
<tr class="memdesc:ga24f8d65c6ffeb2e1468c20f3d1b74a35"><td class="mdescLeft">&#160;</td><td class="mdescRight">Addition of two multivectors. <br /></td></tr>
<tr class="separator:ga24f8d65c6ffeb2e1468c20f3d1b74a35"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ga00f776a1c3d09d2124de69c5014c06e7"><td class="memTemplParams" colspan="2"><a class="anchor" id="ga00f776a1c3d09d2124de69c5014c06e7"></a>
template&lt;class L , class R &gt; </td></tr>
<tr class="memitem:ga00f776a1c3d09d2124de69c5014c06e7"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="structgaalet_1_1subtraction.html">gaalet::subtraction</a>&lt; L, R &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__ga__ops.html#ga00f776a1c3d09d2124de69c5014c06e7">operator-</a> (const <a class="el" href="structgaalet_1_1expression.html">gaalet::expression</a>&lt; L &gt; &amp;l, const <a class="el" href="structgaalet_1_1expression.html">gaalet::expression</a>&lt; R &gt; &amp;r)</td></tr>
<tr class="memdesc:ga00f776a1c3d09d2124de69c5014c06e7"><td class="mdescLeft">&#160;</td><td class="mdescRight">Subtraction of two multivectors. <br /></td></tr>
<tr class="separator:ga00f776a1c3d09d2124de69c5014c06e7"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ga0dd417ff185347c6b44137506692b2a3"><td class="memTemplParams" colspan="2">template&lt;class A &gt; </td></tr>
<tr class="memitem:ga0dd417ff185347c6b44137506692b2a3"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="structgaalet_1_1dual.html">gaalet::dual</a>&lt; A &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__ga__ops.html#ga0dd417ff185347c6b44137506692b2a3">dual</a> (const <a class="el" href="structgaalet_1_1expression.html">gaalet::expression</a>&lt; A &gt; &amp;a)</td></tr>
<tr class="memdesc:ga0dd417ff185347c6b44137506692b2a3"><td class="mdescLeft">&#160;</td><td class="mdescRight">Dual of a multivector.  <a href="#ga0dd417ff185347c6b44137506692b2a3">More...</a><br /></td></tr>
<tr class="separator:ga0dd417ff185347c6b44137506692b2a3"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ga53453f5709f7dffb04af300fbaa3bb36"><td class="memTemplParams" colspan="2">template&lt;class A &gt; </td></tr>
<tr class="memitem:ga53453f5709f7dffb04af300fbaa3bb36"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="structgaalet_1_1exponential.html">gaalet::exponential</a>&lt; A &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__ga__ops.html#ga53453f5709f7dffb04af300fbaa3bb36">exp</a> (const <a class="el" href="structgaalet_1_1expression.html">gaalet::expression</a>&lt; A &gt; &amp;a)</td></tr>
<tr class="memdesc:ga53453f5709f7dffb04af300fbaa3bb36"><td class="mdescLeft">&#160;</td><td class="mdescRight">Exponential of a multivector.  <a href="#ga53453f5709f7dffb04af300fbaa3bb36">More...</a><br /></td></tr>
<tr class="separator:ga53453f5709f7dffb04af300fbaa3bb36"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ga34f97a2b907793b61da13001225f3845"><td class="memTemplParams" colspan="2"><a class="anchor" id="ga34f97a2b907793b61da13001225f3845"></a>
template&lt;class L , class R &gt; </td></tr>
<tr class="memitem:ga34f97a2b907793b61da13001225f3845"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="structgaalet_1_1geometric__product.html">gaalet::geometric_product</a>&lt; L, R &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__ga__ops.html#ga34f97a2b907793b61da13001225f3845">operator*</a> (const <a class="el" href="structgaalet_1_1expression.html">gaalet::expression</a>&lt; L &gt; &amp;l, const <a class="el" href="structgaalet_1_1expression.html">gaalet::expression</a>&lt; R &gt; &amp;r)</td></tr>
<tr class="memdesc:ga34f97a2b907793b61da13001225f3845"><td class="mdescLeft">&#160;</td><td class="mdescRight">Geometric product of two multivectors. <br /></td></tr>
<tr class="separator:ga34f97a2b907793b61da13001225f3845"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ga7b7298b386b1c915ce6d86194296ad26"><td class="memTemplParams" colspan="2"><a class="anchor" id="ga7b7298b386b1c915ce6d86194296ad26"></a>
template&lt;class A &gt; </td></tr>
<tr class="memitem:ga7b7298b386b1c915ce6d86194296ad26"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="structgaalet_1_1scalar__multivector__product.html">gaalet::scalar_multivector_product</a>&lt; A &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__ga__ops.html#ga7b7298b386b1c915ce6d86194296ad26">operator*</a> (const typename A::element_t &amp;s, const <a class="el" href="structgaalet_1_1expression.html">gaalet::expression</a>&lt; A &gt; &amp;a)</td></tr>
<tr class="memdesc:ga7b7298b386b1c915ce6d86194296ad26"><td class="mdescLeft">&#160;</td><td class="mdescRight">Geometric product of a scalar and a multivector. <br /></td></tr>
<tr class="separator:ga7b7298b386b1c915ce6d86194296ad26"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:gafeb3db7c38aa953dbe3661cb600eb6f5"><td class="memTemplParams" colspan="2"><a class="anchor" id="gafeb3db7c38aa953dbe3661cb600eb6f5"></a>
template&lt;class A &gt; </td></tr>
<tr class="memitem:gafeb3db7c38aa953dbe3661cb600eb6f5"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="structgaalet_1_1scalar__multivector__product.html">gaalet::scalar_multivector_product</a>&lt; A &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__ga__ops.html#gafeb3db7c38aa953dbe3661cb600eb6f5">operator*</a> (const <a class="el" href="structgaalet_1_1expression.html">gaalet::expression</a>&lt; A &gt; &amp;a, const typename A::element_t &amp;s)</td></tr>
<tr class="memdesc:gafeb3db7c38aa953dbe3661cb600eb6f5"><td class="mdescLeft">&#160;</td><td class="mdescRight">Geometric product of a multivector and a scalar. <br /></td></tr>
<tr class="separator:gafeb3db7c38aa953dbe3661cb600eb6f5"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ga0f2960b5514dcaa7d027c7289bd1dbe3"><td class="memTemplParams" colspan="2">template&lt;gaalet::conf_t G, class A &gt; </td></tr>
<tr class="memitem:ga0f2960b5514dcaa7d027c7289bd1dbe3"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="structgaalet_1_1grade.html">gaalet::grade</a>&lt; G, A &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__ga__ops.html#ga0f2960b5514dcaa7d027c7289bd1dbe3">grade</a> (const <a class="el" href="structgaalet_1_1expression.html">gaalet::expression</a>&lt; A &gt; &amp;a)</td></tr>
<tr class="memdesc:ga0f2960b5514dcaa7d027c7289bd1dbe3"><td class="mdescLeft">&#160;</td><td class="mdescRight">Projection on a grade of a multivector.  <a href="#ga0f2960b5514dcaa7d027c7289bd1dbe3">More...</a><br /></td></tr>
<tr class="separator:ga0f2960b5514dcaa7d027c7289bd1dbe3"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ga4d5dd9546bf8f7492bbd4f226f5e6a47"><td class="memTemplParams" colspan="2">template&lt;class A &gt; </td></tr>
<tr class="memitem:ga4d5dd9546bf8f7492bbd4f226f5e6a47"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="structgaalet_1_1sinh.html">gaalet::sinh</a>&lt; A &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__ga__ops.html#ga4d5dd9546bf8f7492bbd4f226f5e6a47">sinh</a> (const <a class="el" href="structgaalet_1_1expression.html">gaalet::expression</a>&lt; A &gt; &amp;a)</td></tr>
<tr class="memdesc:ga4d5dd9546bf8f7492bbd4f226f5e6a47"><td class="mdescLeft">&#160;</td><td class="mdescRight">Hyperbolic sine of a multivector.  <a href="#ga4d5dd9546bf8f7492bbd4f226f5e6a47">More...</a><br /></td></tr>
<tr class="separator:ga4d5dd9546bf8f7492bbd4f226f5e6a47"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ga854f54d7ebc422d87b0c88a9a9058238"><td class="memTemplParams" colspan="2">template&lt;class A &gt; </td></tr>
<tr class="memitem:ga854f54d7ebc422d87b0c88a9a9058238"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="structgaalet_1_1cosh.html">gaalet::cosh</a>&lt; A &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__ga__ops.html#ga854f54d7ebc422d87b0c88a9a9058238">cosh</a> (const <a class="el" href="structgaalet_1_1expression.html">gaalet::expression</a>&lt; A &gt; &amp;a)</td></tr>
<tr class="memdesc:ga854f54d7ebc422d87b0c88a9a9058238"><td class="mdescLeft">&#160;</td><td class="mdescRight">Hyperbolic cosine of a multivector.  <a href="#ga854f54d7ebc422d87b0c88a9a9058238">More...</a><br /></td></tr>
<tr class="separator:ga854f54d7ebc422d87b0c88a9a9058238"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ga06c4c2939f5ee987b75edef3fdebbf0a"><td class="memTemplParams" colspan="2">template&lt;class L , class R &gt; </td></tr>
<tr class="memitem:ga06c4c2939f5ee987b75edef3fdebbf0a"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="structgaalet_1_1inner__product.html">gaalet::inner_product</a>&lt; L, R &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__ga__ops.html#ga06c4c2939f5ee987b75edef3fdebbf0a">operator&amp;</a> (const <a class="el" href="structgaalet_1_1expression.html">gaalet::expression</a>&lt; L &gt; &amp;l, const <a class="el" href="structgaalet_1_1expression.html">gaalet::expression</a>&lt; R &gt; &amp;r)</td></tr>
<tr class="memdesc:ga06c4c2939f5ee987b75edef3fdebbf0a"><td class="mdescLeft">&#160;</td><td class="mdescRight">Inner product of two multivectors.  <a href="#ga06c4c2939f5ee987b75edef3fdebbf0a">More...</a><br /></td></tr>
<tr class="separator:ga06c4c2939f5ee987b75edef3fdebbf0a"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ga991a65f7eb76d11702722c0632053256"><td class="memTemplParams" colspan="2">template&lt;class A &gt; </td></tr>
<tr class="memitem:ga991a65f7eb76d11702722c0632053256"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="structgaalet_1_1inverse.html">gaalet::inverse</a>&lt; A &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__ga__ops.html#ga991a65f7eb76d11702722c0632053256">operator!</a> (const <a class="el" href="structgaalet_1_1expression.html">gaalet::expression</a>&lt; A &gt; &amp;a)</td></tr>
<tr class="memdesc:ga991a65f7eb76d11702722c0632053256"><td class="mdescLeft">&#160;</td><td class="mdescRight">Inverse of a multivector.  <a href="#ga991a65f7eb76d11702722c0632053256">More...</a><br /></td></tr>
<tr class="separator:ga991a65f7eb76d11702722c0632053256"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ga4ea137758959348f9b8f1489759e7f54"><td class="memTemplParams" colspan="2">template&lt;class A &gt; </td></tr>
<tr class="memitem:ga4ea137758959348f9b8f1489759e7f54"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="structgaalet_1_1logarithm.html">gaalet::logarithm</a>&lt; A &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__ga__ops.html#ga4ea137758959348f9b8f1489759e7f54">log</a> (const <a class="el" href="structgaalet_1_1expression.html">gaalet::expression</a>&lt; A &gt; &amp;a)</td></tr>
<tr class="memdesc:ga4ea137758959348f9b8f1489759e7f54"><td class="mdescLeft">&#160;</td><td class="mdescRight">Logarithm of a multivector.  <a href="#ga4ea137758959348f9b8f1489759e7f54">More...</a><br /></td></tr>
<tr class="separator:ga4ea137758959348f9b8f1489759e7f54"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:gab33632c76a6cea4cfec70c5659dd1b82"><td class="memTemplParams" colspan="2">template&lt;class A &gt; </td></tr>
<tr class="memitem:gab33632c76a6cea4cfec70c5659dd1b82"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="structgaalet_1_1magnitude.html">gaalet::magnitude</a>&lt; A &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__ga__ops.html#gab33632c76a6cea4cfec70c5659dd1b82">magnitude</a> (const <a class="el" href="structgaalet_1_1expression.html">gaalet::expression</a>&lt; A &gt; &amp;a)</td></tr>
<tr class="memdesc:gab33632c76a6cea4cfec70c5659dd1b82"><td class="mdescLeft">&#160;</td><td class="mdescRight">Magnitude of a multivector.  <a href="#gab33632c76a6cea4cfec70c5659dd1b82">More...</a><br /></td></tr>
<tr class="separator:gab33632c76a6cea4cfec70c5659dd1b82"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ga6dc5352fcc10366b91b92ad2adeaedf3"><td class="memTemplParams" colspan="2">template&lt;class L , class R &gt; </td></tr>
<tr class="memitem:ga6dc5352fcc10366b91b92ad2adeaedf3"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="structgaalet_1_1outer__product.html">gaalet::outer_product</a>&lt; L, R &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__ga__ops.html#ga6dc5352fcc10366b91b92ad2adeaedf3">operator^</a> (const <a class="el" href="structgaalet_1_1expression.html">gaalet::expression</a>&lt; L &gt; &amp;l, const <a class="el" href="structgaalet_1_1expression.html">gaalet::expression</a>&lt; R &gt; &amp;r)</td></tr>
<tr class="memdesc:ga6dc5352fcc10366b91b92ad2adeaedf3"><td class="mdescLeft">&#160;</td><td class="mdescRight">Outer product of two multivectors.  <a href="#ga6dc5352fcc10366b91b92ad2adeaedf3">More...</a><br /></td></tr>
<tr class="separator:ga6dc5352fcc10366b91b92ad2adeaedf3"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ga64a5b4ad2f90749ed92eec3722d47f8f"><td class="memTemplParams" colspan="2">template&lt;gaalet::conf_t... elements, class A &gt; </td></tr>
<tr class="memitem:ga64a5b4ad2f90749ed92eec3722d47f8f"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="structgaalet_1_1part.html">gaalet::part</a>&lt; A, elements... &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__ga__ops.html#ga64a5b4ad2f90749ed92eec3722d47f8f">part</a> (const <a class="el" href="structgaalet_1_1expression.html">gaalet::expression</a>&lt; A &gt; &amp;a)</td></tr>
<tr class="memdesc:ga64a5b4ad2f90749ed92eec3722d47f8f"><td class="mdescLeft">&#160;</td><td class="mdescRight">Projection on a sub-space of a multivector.  <a href="#ga64a5b4ad2f90749ed92eec3722d47f8f">More...</a><br /></td></tr>
<tr class="separator:ga64a5b4ad2f90749ed92eec3722d47f8f"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ga4eb7c5814a703980eb13db09a234f4ec"><td class="memTemplParams" colspan="2">template&lt;class T , class A &gt; </td></tr>
<tr class="memitem:ga4eb7c5814a703980eb13db09a234f4ec"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="structgaalet_1_1part__type.html">gaalet::part_type</a>&lt; T, A &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__ga__ops.html#ga4eb7c5814a703980eb13db09a234f4ec">part_type</a> (const <a class="el" href="structgaalet_1_1expression.html">gaalet::expression</a>&lt; A &gt; &amp;a)</td></tr>
<tr class="memdesc:ga4eb7c5814a703980eb13db09a234f4ec"><td class="mdescLeft">&#160;</td><td class="mdescRight">Projection on a sub-space of a multivector.  <a href="#ga4eb7c5814a703980eb13db09a234f4ec">More...</a><br /></td></tr>
<tr class="separator:ga4eb7c5814a703980eb13db09a234f4ec"><td class="memSeparator" colspan="2">&#160;</td></tr>
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template&lt;class A &gt; </td></tr>
<tr class="memitem:ga509619524507d5e04f37fd44a7919e7c"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="structgaalet_1_1reverse.html">gaalet::reverse</a>&lt; A &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__ga__ops.html#ga509619524507d5e04f37fd44a7919e7c">operator~</a> (const <a class="el" href="structgaalet_1_1expression.html">gaalet::expression</a>&lt; A &gt; &amp;a)</td></tr>
<tr class="memdesc:ga509619524507d5e04f37fd44a7919e7c"><td class="mdescLeft">&#160;</td><td class="mdescRight">Reverse of a multivector. <br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<h2 class="groupheader">Function Documentation</h2>
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<p>Hyperbolic cosine of a multivector. </p>
<p>Only implemented for scalars and bivectors. </p>

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<p>Dual of a multivector. </p>
<p>Depends on metric and should work with a non-degenerate algebra. When operated within degenerate algebra, a positive bilinear form of the corresponding basis vectors is assumed. </p>

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<p>Exponential of a multivector. </p>
<p>Only implemented for scalars and bivectors. </p>

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<p>Projection on a grade of a multivector. </p>
<p>Returns the elements of the multivector belonging to a sub-space of grade G. </p><dl class="params"><dt>Parameters</dt><dd>
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    <tr><td class="paramname">G</td><td>Grade of sub-spaces to project onto. </td></tr>
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<p>Logarithm of a multivector. </p>
<p>Only implemented for scalars, bivectors and spinors. </p>

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<p>Magnitude of a multivector. </p>
<p>Following Hestenes' definition. Undefined for degenerate algebra. </p>

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<p>Inverse of a multivector. </p>
<p>Only implemented for versors. Undefined for degenerate algebra. </p>

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<p>Inner product of two multivectors. </p>
<p>Following Hestenes' defintion. </p>

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<p>Outer product of two multivectors. </p>
<p>Following Hestenes' defintion. </p>

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<p>Projection on a sub-space of a multivector. </p>
<p>Returns the elements of the multivector belonging to a sub-space defined by variadic template parameter <code>elements</code>. <code>elements</code> is a list of configuration bitmaps, e.g. <a class="el" href="group__ga__ops.html#ga64a5b4ad2f90749ed92eec3722d47f8f" title="Projection on a sub-space of a multivector. ">part&lt;1,2,4&gt;()</a>. </p><dl class="params"><dt>Parameters</dt><dd>
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    <tr><td class="paramname">elements</td><td>List of elements defining the sub-spaces to project onto. </td></tr>
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<p>Projection on a sub-space of a multivector. </p>
<p>Returns the elements of the multivector belonging to a sub-space defined by configuration list of multivector <code>T</code>. </p><dl class="params"><dt>Parameters</dt><dd>
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    <tr><td class="paramname">T</td><td>Multivector with configuration list defining the sub-spaces to project onto. </td></tr>
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<p>Hyperbolic sine of a multivector. </p>
<p>Only implemented for scalars and bivectors. </p>

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